There is black semicircle, which radius is $ R $. The red circle is tangentially inward to the semicircle and to the diameter in its center. The yellow on...

How can I prove using an induction technique that an even number plus an odd number is always equals to an odd number? Thanks in advance!

I am in Electronics Technician "A" School in the Navy and we are learning the basics of radars. In one module, we were exposed to this formula which confu...

Today, we had a lecture on Euler line and it's various generalizations/applications. One of the tasks we were given as homework is the following one:...

$A^2$ means to multiple the matrix by itself, and $A^{-1}$ refers to the matrix's inverse. Would $A^{-2}$ be the square of the inverse or the inverse...

What is the remainder when $4^{96}$ is divided by 6 My approach : When 4 is divided by 6 gives 4 remainder, when $4^2$ is divided by 6 gives remainder 4 ,...

How does one create an explicit bijection from the reals to the set of all sequences of reals? I know how to make a bijection from $\mathbb R$ to $\mathbb...

Water is flowing at the rate of 50m^3 per minute from a shallow concrete conical reservoir of base radius 45m and height 6 meters How fast (centimeters pe...

I was confused about the relationship between a set of basis vectors in 3D, $ \left\{\hat e_1, \hat e_2, \hat e_3 \right\} $ and their exterior products. ...

I have an optimization problem where the objective function is $$\text{minimize}_{P \in S_n} ~~ \| PXP'-Y \|_1$$ over the set of permutation matrices...